Question

The mean of 6 numbers is 16. With the removal of a number the mean of remaining
numbers is 17. Find the number removed?
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Answer 1

Given :

• Mean of 6 number = 16
• A number is removed
• Mean after removal of number = 17

To find :

The number removed

Formula used :

Mean = Sum of all observation ÷ number of observation

Solution :

Let -

• Removed number = x
• Sum of other 5 number = y

Part 1)

• Sum of all observation = number removed + sum of other 5 number = x + y
• Number of observation = 5+1 = 6
• Mean = 16

➝ Mean of 6 number = ( Sum of all observation ) ÷ Total number of observation

➩ 16 = ( x+y )/6

➩ x + y = 16×6

➩ x + y = 96

➩ x = 96 - y . . . . equation 1

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Part 2)

• Sum of all observation = sum of other 5 number = y
• Number of observation = 5
• Mean = 17

➝ Mean of 5 number = ( Sum of other 5 observation ) ÷ Total number of observation

➩ 17 = y/5

➩ y = 17×5

➩ y = 85

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Put value of y in equation 1

➝ x = 96-y

➩ x = 96 - 85

➩ x = 11

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ANSWER : 11